213 lines
5.3 KiB
Markdown
213 lines
5.3 KiB
Markdown
Coverage of ReLAPACK
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====================
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This file lists all LAPACK compute routines that are covered by recursive
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algorithms in ReLAPACK, it also lists all of LAPACK's blocked algorithms which
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are not (yet) part of ReLAPACK.
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<!-- START doctoc generated TOC please keep comment here to allow auto update -->
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<!-- DON'T EDIT THIS SECTION, INSTEAD RE-RUN doctoc TO UPDATE -->
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**Table of Contents** *generated with [DocToc](https://github.com/thlorenz/doctoc)*
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- [List of covered LAPACK routines](#list-of-covered-lapack-routines)
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- [`xlauum`](#xlauum)
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- [`xsygst`](#xsygst)
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- [`xtrtri`](#xtrtri)
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- [`xpotrf`](#xpotrf)
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- [`xpbtrf`](#xpbtrf)
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- [`xsytrf`](#xsytrf)
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- [`xgetrf`](#xgetrf)
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- [`xgbtrf`](#xgbtrf)
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- [`xtrsyl`](#xtrsyl)
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- [`xtgsyl`](#xtgsyl)
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- [Covered BLAS extension](#covered-blas-extension)
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- [`xgemmt`](#xgemmt)
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- [Not covered yet](#not-covered-yet)
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- [`xpstrf`](#xpstrf)
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- [Not covered: extra FLOPs](#not-covered-extra-flops)
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- [QR decomposition (and related)](#qr-decomposition-and-related)
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- [Symmetric reduction to tridiagonal](#symmetric-reduction-to-tridiagonal)
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- [Symmetric reduction to bidiagonal](#symmetric-reduction-to-bidiagonal)
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- [Reduction to upper Hessenberg](#reduction-to-upper-hessenberg)
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<!-- END doctoc generated TOC please keep comment here to allow auto update -->
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List of covered LAPACK routines
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-------------------------------
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### `xlauum`
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Multiplication of a triangular matrix with its (complex conjugate) transpose,
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resulting in a symmetric (Hermitian) matrix.
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Routines: `slauum`, `dlauum`, `clauum`, `zlauum`
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Operations:
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* A = L^T L
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* A = U U^T
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### `xsygst`
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Simultaneous two-sided multiplication of a symmetric matrix with a triangular
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matrix and its transpose
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Routines: `ssygst`, `dsygst`, `chegst`, `zhegst`
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Operations:
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* A = inv(L) A inv(L^T)
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* A = inv(U^T) A inv(U)
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* A = L^T A L
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* A = U A U^T
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### `xtrtri`
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Inversion of a triangular matrix
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Routines: `strtri`, `dtrtri`, `ctrtri`, `ztrtri`
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Operations:
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* L = inv(L)
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* U = inv(U)
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### `xpotrf`
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Cholesky decomposition of a symmetric (Hermitian) positive definite matrix
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Routines: `spotrf`, `dpotrf`, `cpotrf`, `zpotrf`
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Operations:
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* L L^T = A
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* U^T U = A
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### `xpbtrf`
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Cholesky decomposition of a banded symmetric (Hermitian) positive definite matrix
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Routines: `spbtrf`, `dpbtrf`, `cpbtrf`, `zpbtrf`
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Operations:
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* L L^T = A
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* U^T U = A
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### `xsytrf`
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LDL decomposition of a symmetric (or Hermitian) matrix
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Routines:
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* `ssytrf`, `dsytrf`, `csytrf`, `chetrf`, `zsytrf`, `zhetrf`,
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* `ssytrf_rook`, `dsytrf_rook`, `csytrf_rook`, `chetrf_rook`, `zsytrf_rook`,
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`zhetrf_rook`
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Operations:
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* L D L^T = A
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* U^T D U = A
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### `xgetrf`
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LU decomposition of a general matrix with pivoting
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Routines: `sgetrf`, `dgetrf`, `cgetrf`, `zgetrf`
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Operation: P L U = A
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### `xgbtrf`
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LU decomposition of a general banded matrix with pivoting
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Routines: `sgbtrf`, `dgbtrf`, `cgbtrf`, `zgbtrf`
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Operation: L U = A
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### `xtrsyl`
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Solution of the quasi-triangular Sylvester equation
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Routines: `strsyl`, `dtrsyl`, `ctrsyl`, `ztrsyl`
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Operations:
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* A X + B Y = C -> X
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* A^T X + B Y = C -> X
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* A X + B^T Y = C -> X
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* A^T X + B^T Y = C -> X
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* A X - B Y = C -> X
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* A^T X - B Y = C -> X
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* A X - B^T Y = C -> X
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* A^T X - B^T Y = C -> X
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### `xtgsyl`
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Solution of the generalized Sylvester equations
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Routines: `stgsyl`, `dtgsyl`, `ctgsyl`, `ztgsyl`
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Operations:
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* A R - L B = C, D R - L E = F -> L, R
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* A^T R + D^T L = C, R B^T - L E^T = -F -> L, R
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Covered BLAS extension
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----------------------
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### `xgemmt`
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Matrix-matrix product updating only a triangular part of the result
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Routines: `sgemmt`, `dgemmt`, `cgemmt`, `zgemmt`
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Operations:
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* C = alpha A B + beta C
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* C = alpha A B^T + beta C
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* C = alpha A^T B + beta C
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* C = alpha A^T B^T + beta C
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Not covered yet
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---------------
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The following operation is implemented as a blocked algorithm in LAPACK but
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currently not yet covered in ReLAPACK as a recursive algorithm
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### `xpstrf`
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Cholesky decomposition of a positive semi-definite matrix with complete pivoting.
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Routines: `spstrf`, `dpstrf`, `cpstrf`, `zpstrf`
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Operations:
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* P L L^T P^T = A
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* P U^T U P^T = A
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Not covered: extra FLOPs
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------------------------
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The following routines are not covered because recursive variants would require
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considerably more FLOPs or operate on banded matrices.
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### QR decomposition (and related)
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Routines:
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* `sgeqrf`, `dgeqrf`, `cgeqrf`, `zgeqrf`
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* `sgerqf`, `dgerqf`, `cgerqf`, `zgerqf`
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* `sgeqlf`, `dgeqlf`, `cgeqlf`, `zgeqlf`
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* `sgelqf`, `dgelqf`, `cgelqf`, `zgelqf`
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* `stzrzf`, `dtzrzf`, `ctzrzf`, `ztzrzf`
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Operations: Q R = A, R Q = A, Q L = A, L Q = A, R Z = A
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Routines for multiplication with Q:
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* `sormqr`, `dormqr`, `cunmqr`, `zunmqr`
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* `sormrq`, `dormrq`, `cunmrq`, `zunmrq`
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* `sormql`, `dormql`, `cunmql`, `zunmql`
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* `sormlq`, `dormlq`, `cunmlq`, `zunmlq`
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* `sormrz`, `dormrz`, `cunmrz`, `zunmrz`
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Operations: C = Q C, C = C Q, C = Q^T C, C = C Q^T
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Routines for construction of Q:
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* `sorgqr`, `dorgqr`, `cungqr`, `zungqr`
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* `sorgrq`, `dorgrq`, `cungrq`, `zungrq`
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* `sorgql`, `dorgql`, `cungql`, `zungql`
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* `sorglq`, `dorglq`, `cunglq`, `zunglq`
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### Symmetric reduction to tridiagonal
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Routines: `ssytrd`, `dsytrd`, `csytrd`, `zsytrd`
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Operation: Q T Q^T = A
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### Symmetric reduction to bidiagonal
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Routines: `ssybrd`, `dsybrd`, `csybrd`, `zsybrd`
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Operation: Q T P^T = A
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### Reduction to upper Hessenberg
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Routines: `sgehrd`, `dgehrd`, `cgehrd`, `zgehrd`
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Operation: Q H Q^T = A
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